To find the coordinates of point B after a 270° rotation about the origin, we apply the standard rotation rule for a 270° counterclockwise rotation. The rule for a 270° counterclockwise rotation of a point $(x, y)$ is:

$(x, y) \rightarrow (y, -x)$

So, if the coordinates of point B are $(x, y)$, the new coordinates after the rotation will be $(y, -x)$.

If we apply this to each option:

• For (4, 2), the new coordinates would be (2, -4), but this is not listed.
• For (2, 4), the new coordinates would be (4, -2), but this is not listed either.
• For (–4, –2), the new coordinates would be (–2, 4), but this is not correct.
• For (–2, –4), the new coordinates would be (–4, 2), which is the correct transformation for the given rotation.

Thus, the correct choice is (–2, –4).

If you'd like more clarification on how to perform rotations or anything else, let me know!

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Here are five related questions for you:

1. How do you perform a 90° rotation of a point about the origin?
2. How would you rotate a point 180° about the origin?
3. What is the general rule for rotating a point counterclockwise by any angle about the origin?
4. Can you apply the rotation rule to a triangle on the coordinate plane? What would the new vertices be?
5. How can you determine the image of a shape after multiple rotations?

Tip: When rotating a point about the origin, always consider the direction of the rotation (clockwise or counterclockwise) and apply the correct formula based on that!